Mathematical Sciences: Algorithms and Existence Theorems forStochastic Games in Finite and Arbitrary State Spaces

该项目涉及随机领域的研究 游戏，处理零和非零和游戏， 有限和任意状态空间。 价值和纳什均衡 在贴现和未贴现的收益都被考虑。 的 以下是该项目的主要问题。 1.找到一个 一种求解无折扣切换控制的有效算法 价值随机博弈和最优平稳策略。 2. 找到一种有效的算法来求解纳什均衡，当 随机博弈是非零和博弈，一个博弈者控制着规则 的运动。 3. 找到一个有效的算法来解决纯 完全信息博弈中的最优平稳策略 或者在具有附加奖励和附加转移的博弈中。 4. 零和随机博弈是否存在最优平稳策略 添加过渡的游戏 5. 做开关控制非- 零和博弈允许静态纳什均衡 6. 他们 拥有秩序场的属性吗 做贴现随机博弈 任意的状态空间和紧的动作空间都具有Nash 静态策略中的均衡，当它们属于 特殊的结构类，如ARAT，一个玩家控制或 切换控制8. 做上述的无折扣零和游戏 结构型在静态策略中具有价值， 空间是任意的吗？

This project concerns research in the area of stochastic games, dealing with both zero-sum and non-zero-sum games in finite and arbitrary state spaces. THe value and Nash equilibria in both discounted and undiscounted payoffs are considered. The following are the main problems of this project. 1. Find an efficient algorithm to solve undiscounted switching control stochastic games for value and optimal stationary strategies. 2. Find an efficient algorithm to solve for Nash equilibria when the stochastic game is non-zero-sum and one player controls the law of motion. 3. Find an efficient algorithm to solve for pure optima; stationary strategies in games with perfect information or in games with additive reward and additive transitions. 4. Are there optimal stationary strategies for zero-sum stochastic games with additive transitions? 5. Do switching control non- zero-sum games admit stationary Nash equilibria? 6. Do they possess order field property? Do discounted stochastic games in arbitrary state space and compact action spaces possess Nash equilibria in stationary strategies when they belong to the special structured class such as ARAT, one player control or switching control 8. Do undiscounted zero-sum games of the above structured type possess value in stationary strategies when the state space is arbitrary?